Procedural Content Generation, continued
2018-04-05 N-3: PCG intro
1. PCG can be used to p____ or a____ game aspects 2. What are some reasons to use PCG? 3. What are some risks / concerns of PCG? 4. Design-time vs run-time PCG? 5. How does the use of a random seed in PCG effect development and gameplay? 6. What is flow theory? How does it relate to dynamic difficulty adjustment & drama management? 7. How do you know you are generating something interesting?
http://jenovachen.com/flowingames/designfig.htm3 N-2: PCG as Search
1. What “search” is happening? Do we seek a path to goal? 2. What is the state space? How many states do we save? 3. How memory efficient is this search? 4. Hill climbing: (PCG as parameter search part 1) 1. L____ search 2. What is the “landscape”? 3. Need a function that maps p____ to f_____ 5. GAs: (PCG as parameter search part 2) 1. Good in ______domains, where _D.K.__ is scarce or hard to encode 2. Can also be used for ____ search 3. Also needs a f_____ function (maps c____ to f_____) 6. Other local search techniques 1. Gradient Descent, Simulated annealing, Local beam, Tabu, Ant Colony Optimization, … N-1: Player models
1. What is a player model? What does it allow? 2. What are two high-level categories of modeling? 3. What are a couple major types within the first category? 4. What are ways to get a player model? Game Bits
Borderlands series No Man’s Sky SpeedTree Game Space
Rogue (1980) Bloodborne, Chalice Dungeons
Spelunky Minecraft Game Scenarios
Skyrim, radiant quests Dwarf Fortress Diablo 2, randomizing situations PCG in General
Indie/AAA games folks use as touchstones • Rogue (1980) • Dwarf Fortress (2006) • Minecraft (2009) • Spelunky (2012) • No Man’s Sky (2016) • Stolen terms (bits, space, scenarios): Procedural Content Generation for Games: A Survey • https://course.ccs.neu.edu/cs5150f13/readings/hendrikx_pcgg.pdf • Search-Based Procedural Content Generation: A Taxonomy and Survey • https://course.ccs.neu.edu/cs5150f13/readings/togelius_sbpcg.pdf • PCG in Games: A textbook and an overview of current research (2016) • http://pcgbook.com • http://pcg.wikidot.com/
Content is king! PROCEDURAL CONTENT GENERATION
10 PCG high-level Methods
• Search • Rule systems • Generative Grammars • Constraint Solving
11 http://pcgbook.com/wp-content/uploads/chapter02.pdf JUMPED IN TO SEARCH ALREADY…
12 Genetic Algorithms
• Loosely inspired by Darwin’s Theory of Evolution • Sometimes called “Evolutionary search” • Consistently pretty popular (if only for the tagline “evolving artificial intelligence to solve…”)
13 Genetic Algorithm Pseudocode population = set of random points of size X time = 0 while E(population) 14 GA Pseudocode cont • Mutate: Given some probability, randomly replace a member of the population with a neighbor – Make a random change • Crossover: Take pairs of the initial population (chosen based on fitness), and combine their features randomly till population grows up to size Y (where X 15 Genetic Algorithms Pros – Middling authorial burden (more than hill climbing, less than generative grammars/rule system) – High likelihood of finding global optima-ish Cons – Takes skill to pick and balance mutation/crossover – Over-reliance 16 Search-based PCG Pros – Allows for designers to specify high-level desires in heuristics rather than low level content authoring Cons – Coming up with a good heuristic is hard – Many devs will prefer to just use generative grammars 17 PCG: RULE SYSTEMS 18 PCG high-level Methods • Search • Rule systems • Generative Grammars • Constraint Solving 19 Rule Systems • Similar to the rule systems discussed before – If (world has certain conditions) – Then (make change to world) • Now focused on building game bits/spaces, with each rule focusing on one feature – Example: if y 20 Rule Systems Methods Cellular Automaton 1. Take noise/random values 2. segment bits/space into grids 3. Each grid updates until stable/time limit Agent-based simulation 1. Take noise/random values 2. Iterate each agent over the world 3. Continue until stable/time limit Where are the rules? In each grid cell (cellular automaton) or in an agent (agent-based simulation) 21 Quick note: Noise > Random Sin wave Pure “random” Perlin noise 22 Cellular Automaton Stanislaw Ulam and John von Neumann (1940) Conway’s Game of Life made famous (1970s) Rules: 1. Any live cell with fewer than two live neighbors dies, as if caused by underpopulation. 2. Any live cell with two or three live neighbors lives on to the next generation. 3. Any live cell with more than three live neighbors dies, as if by overpopulation. 4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction. 23 Cellular Automaton Example https://www.youtube.com/watch?v=OumDj9PN WjE 24 Cellular Automaton Pros – Easy to implement – Complex behavior from small set of rules – Intuitive mapping to game space generation – Local coherence Cons – Reliant on guess and check for modifying – Hard to spot edge cases – No way to forbid undesired output – Upper bound is slow – Global incoherence 25 Question Cellular Automata are good at local coherence and bad at global coherence, which limits its usage cases (caves, mazes, etc). What could we add or change to this approach to allow for a designer to ensure global coherence? 26 What if… • What if we had another set of rules, not for a single grid cell, but for the whole grid? • Well, in that case we don’t have to use a grid at all. All the rules could be on this layer • And we could even have rules that contradict one another, so we’d get… 27 Agents • Instead of individual grid rules, have multiple agents that iteratively update a map. – Example: • Mountain agent: make high points higher • Valley agent: flatten out sections • River agent: make low points lower and add water • Manager: make parts of the map non-editable when they reach thresholds • Harder to come up with rulesets that converge completely on their own, so dependent on time 28 Comparisons: CA vs Agents • Similarities (rule system commonalities): – Rely on “emergent” output of simple rules – Hard to make strong designer restrictions – Requires a lot of guess and check – Can take a long time to converge • Differences – Agents allows for some global assurances – CA more emergent in its output 29 Major Drawback of Rule Systems • What cellular automaton could you construct to build a house? A sword? An NPC? – Local rules don’t adapt well to generating bits that require strong global coherence – Said another way, no one wants an NPC that only looks locally like a human 30 http://pcgbook.com/wp-content/uploads/chapter05.pdf PCG: GENERATIVE GRAMMARS 31 PCG high-level Methods • Search • Rule systems • Generative Grammars • Constraint Solving 32 Solution: Generative Grammars • Noam Chomsky’s study of languages in the 1960s – Rich taxonomy of grammars – Widespread application • Key questions: determinism & order of expansion • Components with rules about how they are allowed to be put together – Words that can be placed together in a sentence according to grammar rules – Limbs that can be combined to form creatures according to designer rules http://pcgbook.com/wp-content/uploads/chapter05.pdf 33 Formal Grammars • Grammar: set of production rules for rewriting strings – Rule: 34 Determinism & Order • Determinism – Deterministic grammar: one rule that applies to each symbol or sequence – Nondeterministic grammar: several rules may apply • Random • Probabilities & Priors • Rewriting order – Sequential: left to right, rewrite string while reading it – Parallel: all rewriting done at same time 35 L-systems • Class of grammars w/ parallel rewriting • Aristid Lindenmayer, 1968: model growth of organic systems • EG (Given A): A AB B A – A – AB – ABA – ABAAB – ABAABABA – ABAABABAABAAB 36 Application and Interpretation • One approach: interpret strings as drawing instructions – F: move forward 10 pixels – L: turn left 90 – R: turn right 90 content/uploads/chapter05.pdf – EG: F F L F R F R F L F - http://pcgbook.com/wp 37 Bracketed L-systems • How do we “lift the pen”? – Plants are branching, and branches end • Introduce two extra symbols: ‘[‘ and ‘]’. A FILO stack – [ push content/uploads/chapter05.pdf – ] pop - • EG: F F[RF]F[LF][F] http://pcgbook.com/wp 38 Beyond strings • Generative grammars are not restricted to representation as strings – Graphs, tile maps, 2D/3D shapes, etc. • Graph grammar: – Find subgraph in target that matches LHS; mark subgraph w/ IDs – Remove all edges between marked nodes – Transform marked nodes into corresponding RHS • Add a node for each node on RHS not present in target • Remove any nodes that have no corresponding node on RHS – Copy edges as specified by RHS – Remove all marks http://pcgbook.com/wp-content/uploads/chapter05.pdf Example: Spelunky Levels • Each Spelunky level starts life as a grid. • Each grid can be filled in with potential templates designed by Derek Yu (designer) • Templates are filled in one by one • Later templates chosen according to rules about how templates can neighbor Game Maker’s Toolkit: https://www.youtube.com/watch?v=Uqk5Zf0tw3o 40 Generative Grammars • Generative grammars are well-suited to both game bits and game spaces – Borderlands’ guns – Bloodborne’s chalice dungeons • …but they are only as good as the components and rules the designer creates – No man’s sky’s ship and creature generation 41 Generative Grammars Pros: – General usage – High-quality, “feels designed” quality – Accessible – Fast • Cons: – Large burden on design – Hard to “debug” • How do you know if a fix actually fixed anything unless you generate infinite output? 42 Comparing the Approaches • Rule Systems allow for emergent output from simple rules. But hard to control output. • Generative grammars can create high-quality output, but depend upon expert authoring of components and rules • Search cuts back on authoring burden to just a heuristic and searchable representation, but these are unintuitive for many designers See http://pcgbook.com/wp-content/uploads/chapter07.pdf PCG: CONSTRAINT SOLVING & PLANNING 44 Constraint Satisfaction • Also called constraint solving/constraint propagation • Similar to search but instead of a heuristic with a single value, designers give constraints – Constraints are facts that must be true in the final “answer” output – Constraints can be authored or learned from an example • Shout out to Dr. Adam Smith at UCSC Constraint Satisfaction Problem (CSP) Input – Set of variables/slots – Set of all values that can go in the slots – Set of constraints that relate slots to each other Output – All variables are filled with a specific value Trivial Example: Name generator – Variables: • Initially, all variables have a list of all values they could potentially have • Each update, pick one variable and choose arbitrarily from its remaining values (collapse) • Based on the constraints, remove values from the surrounding variables to represent that they are no longer possible (propagation) • End when all variables have only one value CSP related to Search/Planning • We have seen the idea of iteratively solving constraints before in partial order planning – Use similar heuristics: most constrained variable, minimum remaining values • CSP is essentially search, but is generally faster as we cut out vast parts of the search space due to constraint propagation CSP: Dungeon Room Example 1-4 E 1-4 1-4 Constraints: 1-4 1-4 1-4 1-4 • There must be a path from the entrance to 1-4 1-4 1-4 1-4 all treasure and all 1-4 1-4 1-4 1-4 enemies • There can only be at Values: most 1 treasure 1. Blank • There can only be at 2. Wall most 2 enemies 3. Enemy • Enemies cannot be 4. Treasure next to each other CSP Step 1 Collapse: 1-4 E 1-4 1-4 Constraints: 1-4 1-4 1-4 1-4 • There must be a path 1-4 1-4 1-4 1-4 from the entrance to all treasure and all 1-4 1-4 1-4 enemies Propagate: • There can only be at 1-4 E 1-4 1-4 most 1 treasure 1-4 1-4 1-4 1-4 • There can only be at most 2 enemies 1-4 1-4 1,2, 1-4 4 • Enemies cannot be 1-4 1,2,4 1,2, next to each other 4 CSP Step 2 Collapse: 1-4 E 1-4 1-4 Constraints: 1-4 1-4 1-4 1-4 • There must be a path 1-4 1-4 1,2, 1-4 from the entrance to 4 all treasure and all 1-4 1,2, enemies 4 Propagate: • There can only be at 1-3 E 1-3 1-3 most 1 treasure 1-3 1-3 1-3 1-3 • There can only be at most 2 enemies 1-3 1-3 1,2 1-3 • Enemies cannot be 1-3 1,2 next to each other CSP Step 3 Collapse: 1-3 E 1-3 1-3 Constraints: 1-3 1-3 1-3 1-3 • There must be a path 1-3 1-3 1-3 from the entrance to all treasure and all 1-3 1,2 enemies Propagate: • There can only be at 1-3 E 1-3 1-3 most 1 treasure 1-3 1-3 1-3 1,3 • There can only be at most 2 enemies 1-3 1-3 1,3 • Enemies cannot be 1-3 next to each other CSP Output E E E E E E CSP Usage If output doesn’t look good, just add more constraints! – Don’t have to consider balancing heuristic Need to strike balance of overly constrained/avoiding bad output – In general, designers prefer this over heuristic tuning Question 1 • Come up with a very simple generation task to which you could apply constraint satisfaction – Give the variables for the problem – Give the values for those variables – Give the constraints Writing constraints seems hard Didn’t you say constraints could be learned? Wave Function Collapse Wave Function Collapse: The New Hotness Proc Skater, Joseph Parker (2016) Caves of Qud, Freehold Games (2016) https://github.com/mxgmn/WaveFunctionCollapse WaveFunctionCollapse is Constraint Solving. 2017. Workshop on Procedural Content Generation Wave Function Collapse Big Ideas 1. Derive legal patterns from a sample input 2. Determine legal intersections of patterns to get constraints Wave Function Collapse Algorithm PatternsFromSample() BuildPropagator() Novel Stuff While notFinished: Observe() Classic Constraint Satisfaction Propagate() OutputObservations() Patterns from Sample (given neighbor size N=2) The larger the neighbor size, the more like the input sample Build Propagator Output CSP Pros/Cons Pros • Constraints are more intuitive than heuristics • Faster in many cases than search – Though slower than grammars due to propagation • Can learn constraints from exemplar Cons • Must be able to represent problem in terms of formal logic Story/Quests in Games Story: Series of events players experience • Linear: players experience the same story • Multilinear/Non-linear: players experience variations on the same story based on choices Quests: Give the player something to do for experience points, challenge, or the story Why would we want to generate these? • Add more content to a game • Create new types of game experiences – More on this in the third PCG lecture Quest Generation: Templates • We can create a quest template based on standard quest types or to fulfill a specific in-game purpose • Example: Assassination: Go to • Variables: like • Generation is then trivial random selection Quest Templates Example: Bethesda • Collect values of types (LOCATION, NPC, etc) once the player has visited or been made aware of them • On generation select a template and fill in with values from these types Quest Templates Pros • Fast (basically a generative grammar) • Can be customized to player experience Cons • Basically madlibs where you do the same madlib over and over again • Gets boring quickly Story Generation • Templates • Planning (forward, backward, POP, HTN) • Talespin (1992) 75 http://pcgbook.com/wp-content/uploads/chapter07.pdf Plan-Story Examples Planner Approaches • Agent-based: Each agent is a planner, comes up with plans. Replan if they break – State: Current local state to an agent – Actions: Actions that agent is capable of • Narrator-based: High-level story plans, with a much larger search space – State: The entire current story state (characters, locations, items, etc) – Actions: Everything any character or the world could do Story Domain • The model of possible actions, locations, characters that can occur from a specific domain • This must be authored by a designer instead of a typical story to use one of these approaches Question 2 This all works well for a linear story, but what if we wanted to make a multilinear/non-linear story? My Answer • Well really Fred Charles, Marc Cavazza and Steven Mead’s answer • Hierarchical Task Networks – Replan just the chunks of the story the player messes up • Examples – https://www.youtube.com/watch?v=0erFey9hQTY – https://www.youtube.com/watch?v=3wzSb8fzDA4 Story Planning Pros: • Many possible stories • Can adapt to the player Cons: • Slow • Hard to get heuristics right (optimal stories rarely interesting) From AI Game Programming Wisdom 2 (Rabin, 2004) CASE STUDY: EMPIRE EARTH (SHOEMAKER’S MAPMAKER) • Dedicated exclusively to designing RTS games • RT 3D game engine: TITAN 2.0 – Windows, complete source (c++), 40+ person years – 3 million units sold (got cash?) • Empire Earth – Released Nov 2001 – “… a new high-water mark for realtime strategy fans.” GameSpy’s Dave Kosak – Same lead game designer (Rick Goodman) as AOE • Empires: Dawn of the Modern World 84 Birds-Eye 85 Fancy 3D View 86 If You Were Asked… • Make a system to generate maps – Tile-based – RTS – Multi-player • What qualities should these maps have? 87 These Maps Must be ______? • Fair • Reproducible – Land per player – Seed & type & size – Resources per player – Number of players – No strategic advantage • Varied • Predictable – Size – Similar by type – Type – Allow for diff. outcomes • Relatively Quick – Many in-game systems not running – Impatient to start 88 Shoemaker’s Mapmaker • 1 .dll & 50+ script files • Different .dll can be specified • 7 scripts for each map type • Inputs – # players, # teams – Size – Climate – Type – Random # seed 89 Intermediate Results • Visualization tool created for 2D arrays – Land/Water – Height – Height/Water – Combined • Map engine integrated late into game 90 91 Solution Overview • Step 1: Place players (blank map of H2O) 92 Solution Overview • Step 2: Grow player land 93 Solution Overview • Step 3: Add flatlands to map 94 Solution Overview • Step 4: Generate elevations map 95 Solution Overview • Step 5: Combine the two (obeying rules) 96 Solution Overview • Step 6: Fix cliffs and other anomalies 97 Solution Overview • Step 7: Distribute resources to players • Step 8: Place trees • Step 9: Paint map with terrain textures • Step 10: Place initial units for players • Step 11: Place wildlife • Steps 9 through 11 won’t be covered. 98 Step 1: Details • Placement directly effects land growth • How would you do this? • Algorithm: – Inscribe one large disk onto map – Assign one random loc. per player w/in disk – Repeatedly push closest of player points apart until distribution sufficiently optimal • “optimal” is a map attribute • Specifies how evenly players must be placed 99 Step 1: Results • Predictable player locations. Desirable? – Keeps maps balanced – Tunable through map attributes • Assign player to points after placed. Why? – Teams adjacent to each other – Enemies somewhat symmetrically opposed • What about colonization? “Dummy” players… – Placed after real players, on in/outside of disk. Why? – Dummies’ land grown after real players. Why? – Give the dummies resources too. 100 Step 2: Details • Land is a resource in RTS games! – Allocate fairly – Must appear “natural” • Clumps, modifiable script attributes – clumpSize – clumpNumber – Chaos level • World starts as H2O • What’s a clump? 101 Step 2: Clumps • Grow until – size == clumpsize • Create new clump some dist away at random, chaotic angle – Can’t grow any larger • Make new clump of limited size • Continue until number == clumpNumber • Two growth methods, step & completion 102 Step Clump Growth • 1st tile is players starting location • Choose one valid random edge per iteration 103 Valid Clumps • Different types have different rules – Don’t take owned land – Don’t make peninsulas • Island Clumps: 104 Step Clump Discussion • Why is stepwise growth desirable? – Fair • each player has equal chance to grow – Preventative • Hinders one’s land “surrounding” another’s • Avoids “starvation” – Opportune • Makes good on the importance of placing players! • Remember the dummies! 105 Completion Clumps • Why bother, steps are awesome?! • How about step 3? 106 Step 4: Details • 2D height map array • Fractals (esp. diamond sq.) – Quick & easy – Realistic looking elevation • Once again, map attributes – Min, max, initial elevation • What about “noise”? – Filter used to smooth out jagged artifacts 107 Step 5: Details • Remember “obeying rules”? • Algorithm: – if( landNH2O[i][j] == FLAT ) ignore heightMap – if( landNH2O[i][j] == LAND && height[i][j] == WATER ) • Raise value in height[i][j] to preserve natural look – if( landNH20[i][j] == WATER && height[i][j] == LAND ) • Lower height[i][j] to landNH2O[i][j] level • Why not negate in the last two cases? 108 Step 6: Details • We’ve got anomalies again! • Wouldn’t negating have worked? • Re-apply filter 109 Step 7: Resource Allocation • Each player gets same amt. of each w.r.t. other players • Randomly placed within rings centered on players’ starting locs. • Validation – Some resources can’t be placed on terrain features – Resources restricted in min. distance to other resources – Resources restricted in min. dist to start loc • Once again, map attributes – Amount of each resource – Size of ring 110 Step 8: Place trees • Plentiful; Restrict pathfinding • Can the clump class be re-used? • Map attributes – Number forests/player – Size of forests – Number of clumps/forest • Some areas of map marked as forest free • Player-owned land does not restrict growth 111 Scripts • Language to manipulate map attribs • Basic text parser and data structures • Things like: – #resources per player – Max altitude in height map – Player land allocation – Climate (terrain/forest/animal texture set) • Small changes yield map variations 112 Scripts: Pros • Allow for incremental map type devel. – New attribs for new maps – Add attribs to parser – Matching code added to map generator – Offload some tasks from programmers to designers – Modability/extensibility/variety • Next steps… – Island map w/teams: allow land for team-members to merge – Tweak elevations: island maps become canyon maps – Tweak clump size: island maps become river maps 113 Scripts: Cons • Unfortunately: – One master script per type of random map – One script per size of type of map – In each script, subsections for each qty. of players (# berries? # gold?) • You can imagine: – Scripts can become hard to manage – Manuals needed to explain types & attribs – Additional tools to edit attribs across files – Designers are not programmers • Programmers must create map “templates” • Designers simply “tweak” 114 Buyer Beware! • Can’t explicitly place particular terrain features – “super-tile” design approach – Fairer/more visually appealing • Designers are not programmers • Chokepoints are possible & unfair • Resource placement can still yield advantages 115